Question

Numbers inside a parenthesis is a fraction, the / being the division bar. Solve for x:

(1/x+6)-(4/x)=(2x+6/x^2+6x)

Answer 1

Is it:

\(\large\frac{1}{x+6} - \frac{4}{x} = \frac{2x+6}{x^2 + 6x}\)

Answer 2

yeah that's it. sorry, i'm brand new to this site so i don't know how to make the equation look like that lol

Answer 3

You don't need to know how to do that just yet, however, you should at least know how to write fractions linearly

Answer 4

1/(x+6) - 4/x = (2x+6)/(x^2+6x)

How you place the parentheses are important

Answer 5

I will post a solution soon

Answer 6

ok thank you

Answer 7

0. Given

\(\frac{1}{x+6} - \frac{4}{x} = \frac{2x+6}{x^2 + 6x}\)

1. Multiply 1/(x+6) by x/x:
\(\frac{x}{x^2+6x} - \frac{4}{x} = \frac{2x+6}{x^2 + 6x}\)

2. Subtract x/(x^2 + 6x) from both sides:
\( - \frac{4}{x} = \frac{2x+6}{x^2 + 6x} - \frac{x}{x^2+6x}\)

3. Combine the right side:
\( - \frac{4}{x} = \frac{2x+6 - x}{x^2 + 6x}\)

4. Simplify the right side:
\( - \frac{4}{x} = \frac{x+6}{x^2 + 6x}\)

5. Factor the denominator of the right side fraction:
\( - \frac{4}{x} = \frac{x+6}{x(x + 6)}\)

6. Cancel the factor of 1 (x+6)/(x+6):
\( - \frac{4}{x} = \frac{1}{x}\)

7. Cross mulitply:
\(\small-4x = x\)

8. Add 4x to both sides:
\(\small4x + x = 0\)

9. Combine the left side:
\(\small5x = 0\)

10. Divide both sides by five:
\(\small x = \frac{0}{5}\)

11. Solution
\(\small x \ne 0\), therefore no solution.

Answer 8

Thanks! That helps a lot.

Answer 9

Yeah, I double checked \(x \ne 0\), so no solution.